Spectral characterization of line graphs of starlike trees

摘要

Two graphs are said to be A-cospectral if they have the same adjacency spectrum. A graph G is said to be determined by its adjacency spectrum if there is no other non-isomorphic graph A-cospectral with G. A tree is called starlike if it has exactly one vertex of degree greater than 2. In this article, we prove that the line graphs of starlike trees with maximum degree at least 12 are determined by their adjacency spectra.